SOLUTION: Write the equation of the line passing through each of the given pairs of points. Write results in slope intercept form. (-1,3), (4,-2) Thanks for any help I am a 30 yr old sing

Algebra ->  Linear-equations -> SOLUTION: Write the equation of the line passing through each of the given pairs of points. Write results in slope intercept form. (-1,3), (4,-2) Thanks for any help I am a 30 yr old sing      Log On


   

Question 107869: Write the equation of the line passing through each of the given pairs of points. Write results in slope intercept form. (-1,3), (4,-2) Thanks for any help I am a 30 yr old single mom returning to school after many years and OH my I am LOST.
thanks again
Heather
Found 2 solutions by DID YOU SAY MATH?, jim_thompson5910:
Answer by DID YOU SAY MATH?(1) About Me  (Show Source):
You can put this solution on YOUR website!
you know,this might not be thee right answer but....
-2-3 and 4-(-1) O.O plz dont blame me if this is wrong.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (-1,3) and (4,-2)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (-1,3) and (x%5B2%5D,y%5B2%5D) is the second point (4,-2))


m=%28-2-3%29%2F%284--1%29 Plug in y%5B2%5D=-2,y%5B1%5D=3,x%5B2%5D=4,x%5B1%5D=-1 (these are the coordinates of given points)


m=+-5%2F5 Subtract the terms in the numerator -2-3 to get -5. Subtract the terms in the denominator 4--1 to get 5




m=-1 Reduce



So the slope is

m=-1





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Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and (x%5B1%5D,y%5B1%5D) is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


y-3=%28-1%29%28x--1%29 Plug in m=-1, x%5B1%5D=-1, and y%5B1%5D=3 (these values are given)



y-3=%28-1%29%28x%2B1%29 Rewrite x--1 as x%2B1



y-3=-x%2B%28-1%29%281%29 Distribute -1


y-3=-x-1 Multiply -1 and 1 to get -1%2F1. Now reduce -1%2F1 to get -1

y=-x-1%2B3 Add 3 to both sides to isolate y


y=-x%2B2 Combine like terms -1 and 3 to get 2

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Answer:



So the equation of the line which goes through the points (-1,3) and (4,-2) is:y=-x%2B2


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1 and the y-intercept is b=2


Notice if we graph the equation y=-x%2B2 and plot the points (-1,3) and (4,-2), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=-x%2B2 through the points (-1,3) and (4,-2)


Notice how the two points lie on the line. This graphically verifies our answer.